Math 228A, Numerical Solutions of Differential Equations, Fall 2014.

## Math 228A, Numerical Solutions of Differential Equations, Fall 2014.

Description: This course focuses on numerical solutions and theoretical treatment of differential equations and integral equations. Topics include
• Runge-Kutta methods and multistep methods.
• Stability theory.
• Stiff ODEs.
• direct and iterative linear equation solvers.
• Finite difference methods for elliptic problems.
• Fast solutions of boundary integral equations.
Prerequisite: Math128A or equivalent for basic analysis and some MATLAB experience for progamming skills.
Lecturer: Ming Gu, mgu@berkeley.edu, 861 Evans, Phone (510) 642-3145
Office hours: MF 1:00-2:00pm and W 2:00-3:00pm in 861 Evans.
GSI: Luming Wang, lwang@berkeley.edu
Office hours: M 4:00-6:00PM, 1085 Evans.
Grading: Grades will be based on bi-weekly problem sets, some of which can be quite challenging or time consuming. While discussions with other students in the class are allowed, the work you handle in must be entirely your own (both solutions and MATLAB codes).
Syllabus: This syllabus is frequently updated to keep up with the pace of the class.

01 Fri. 08/29 Overview, ODEs (IVPs, BVPs), PDEs
02 Wed. 09/03 Finite Difference Approximations L:1.1-1.5, PDF1
03 Fri. 09/05 Boundary Value Problems L2.1-2.10
04 Mon. 09/08 Boundary Value Problems L2.11 -- 2.14
05 Wed. 09/10 Boundary Value Problems L2.15-2.16
06 Fri. 09/12 Boundary Value Problems L2.1-2.10
07 Mon. 09/15 Boundary Value Problems L2.17-2.20
08 Wed. 09/17 Boundary Value Problems L2.20-2.21, Integral Equation Solutions to TPBVP
09 Fri. 09/19 Elliptic Equations L3.1-3.4, Nested_Dissection
10 Mon. 09/22 Elliptic Equations L3.5-3.7
11 Wed. 09/24 Elliptic Equations L3.5-3.7
12 Fri. 09/26 Elliptic Equations L3.5-3.7
14 Wed. 10/01 GMRES Method L4.4, GMRES Method
15 Fri. 10/03 Multigrid Method L4.6, Multigrid Tutorial
16 Mon. 10/06 Initial Value Problems L5.1-5.6
17 Wed. 10/08 Initial Value Problems L5.7
18 Fri. 10/10 Initial Value Problems L5.8-5.9

Problem sets:
HWK Due Date Assignment
Homework Set 1 Mon Sept. 15, 2014 PDF
Homework Set 2 Mon Sept. 29, 2014 PDF
Homework Set 3 Mon Oct. 20, 2014 PDF
Homework Set 4 Mon Nov. 3, 2014 PDF
Homework Set 5 Mon Nov. 24, 2014 PDF
Homework Set 6 Fri Dec. 12, 2014 PDF
MATLAB Codes:
Lecture Code
Lecture 2 Finite Difference Approximations, fdcoeffF.m, bvp_2.m
Homework Set 4 Solving ODEs with RK methods: erk1ml.m, erk2.m , erk1
Homework Set 5 tplot.m, boundary_nodes.m.